By T. Goodall
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Additional resources for Adequate Decision Rules for Portfolio Choice Problems
Decision rules may be characterised accordingly. 2 Rather than utilising all information provided by the entire distribution of a gamble, classical decision rules utilise only some distribution parameters, like the mean, the median or the variance. The parameters alone determine which alternative to 15 A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS choose. Although classical decision rules were at times considered mere approximations to decision rules which make use of the entire distribution,3 they may be treated as decision rules in their own right.
It should indeed be called a decision principle, rather than a decision rule. Until the function ϕ(u) is speciﬁed, the EU principle may recommend or describe vastly different decision behaviour. The EU principle’s widespread acceptance is due to the axiomatic embedding it has received, which goes beyond the axioms of linearity, reﬂexivity and transitivity. These axioms provide for the existence of a general function that indicates preferences among unspeciﬁed elements 24 of a general set. The axioms designed for the normative justiﬁcation of the EU principle provide both for the existence of the risk attitude function ϕ(u) and for the mathematical form of the decision principle itself.
This does remedy the lack of subjectivity mentioned above. He proposes utilities that are proportional to the gains and inversely proportional to the wealth of the gambling individual, thus arriving at a logarithmic utility function of money 21 chapter three A N A LY S I S O F P R O M I N E N T DECISION RULES A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS wealth. Bernoulli’s rule thus replaces a one-to-one utility function u(r) = r by a logarithmic utility function, which in the general case can be written as u(r) = b⋅ln(r), where ln is the natural logarithm, and where b serves as a coefficient characterising the individual.